A288314 - OEIS

%I #5 Jun 09 2017 19:39:44

%S 0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,

%T 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,

%U 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0

%N Fixed point of the mapping 00->0001, 1->00, starting with 00.

%H Clark Kimberling, <a href="/A288314/b288314.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 0001

%e 0001000

%e 000100000010

%e 0001000000100010001000

%e 0001000000100010001000001000000100000010

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0001", "1" -> "00"}]

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48   (* A288314 *)

%t Flatten[Position[st, 0]]  (* A288315 *)

%t Flatten[Position[st, 1]]  (* A288316 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288317 conjectured *)

%Y Cf. A288315, A288316, A288317.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 09 2017